# Mathematics Algebra Seminar: Lisa Marquand, Finite groups of symplectic birational transformations o

This event is in the past.

**When:**

October 3, 2023

1 p.m. to 2 p.m.

1 p.m. to 2 p.m.

**Where:**

Nelson Library, Faculty Administration Bldg
#1146

**Event category:**Seminar

In-person

**Speaker**: Lisa Marquand

**Institution**: NYU: Courant Institute

**Title**: Finite groups of symplectic birational transformations of manifolds of OG10 type

**Abstract**: Compact Hyperkähler manifolds are one of the building blocks of Kähler manifolds with trivial first chern class, but very few examples are known. One strategy for potentially finding new examples is to look at finite groups of symplectic automorphisms of the known examples, and study the fixed loci or quotient. In this talk, we will classify saturated finite groups of birational symplectic transformations of manifolds of OG10 type. In particular, there are 209 possible finite groups that occur, with 64 of those having unique action on cohomology. We provide a criteria for when such a group is obtained from a cubic fourfold via the compactified intermediate Jacobian construction. If time permits, we will mention ongoing work to identify the fixed loci in one of these examples. This talk is based on joint work with Stevell Muller.